KETO-CTA Study

An Audit with the Actual Data

John | The John & Calvin Podcast

Dataset of Plaque Metrics

Longitudinal Data From the KETO-CTA Study: Plaque Predicts Plaque, ApoB Does Not

Released by organization funding the study:

https://citizensciencefoundation.org/keto-cta/

All code, figures, data, studies available at:

https://github.com/SloughJE/keto_cta_analysis_check

Incorrect Figure 1B

Figure 1B from Study

Figure 1B from Data

Individual Change in Plaque Volume

(B) The red line represents the median change (0.8%), and the shaded area represents the IQR (0.3%-1.7%).

  x     y

q25 1 15.5 q75 2 25.2

q25 1 102. q75 2 163.

Incorrect Figure 1A

Figure 1A from Study

Figure 1A from Data

Individual Change in Plaque Volume

(A). The red line represents the median change (18.9 mm3), and the shaded area represents the IQR (9.3-47.0 mm3).

Incorrect Figures 2D, 2E, 2F

Figure 2F from Study

Figure 2F from Data

Changes in Total Plaque Score vs Coronary Artery Calcium

(C, F) Only CAC is associated with changes in NCPV and TPS. The regression line was fitted with the function “lm,” which regresses y~x, and the shaded area represents the standard error.

Linear Model Assumptions

4 Simple Linear Regression Assumptions

3 are tested with data

Linearity: between the predictor and the outcome
Constant variance (homoscedasticity) of residuals
Normally distributed residuals

These linear assumptions are quantifiable and objectively testable.

If the assumptions don’t hold, statistical significance and uncertainty estimates aren’t trustworthy
Results may be invalid

LM Assumptions (claims vs tests)

“all linear model assumptions were corroborated with the R function performance::check_model.”

- Direct quote from the study

Actual Linear Model Assumption Tests

Model	β	Linearity	Constant Variance	Residual Normality
ΔNCPV ~ CAC_bl	β = 0.18 p = <0.001	Violation p = 0.031	Violation p = 0.001	Violation p = <0.001
ΔNCPV ~ NCPV_bl	β = 0.25 p = <0.001	OK p = 0.198	Violation p = <0.001	Violation p = <0.001
ΔNCPV ~ PAV_bl	β = 5.48 p = <0.001	Borderline p = 0.050	Violation p = <0.001	Violation p = <0.001
ΔNCPV ~ TPS_bl	β = 7.37 p = <0.001	OK p = 0.132	Violation p = <0.001	Violation p = 0.001

Objective tests show all 4 models failed at least 2 tests.

Letter to Editor and Response

“The validity of the regression models is also questionable. Despite claims of meeting assumptions, variables were reported using medians, suggesting non-normal distributions. Visual inspection of scatter plots shows clustering and no clear linear trends. Robust or nonparametric methods might have been more appropriate, and model diagnostics would improve transparency.”

- quote from letter to the editor

“we are aware of the relevance of linear assumptions to obtain accurate estimators. Because residual plot evaluation can also be subjective, we followed their suggestion and reran all models with robust linear regression (using the MASS::rlm function in R version 4.4.3 [R Foundation]). While, as expected, there were small differences with the published estimates, all models using robust regression were consistent with what was reported.”

- quote from the reply to a letter to the editor

“residual plot evaluation can also be subjective”

- quote from the reply to a letter to the editor

“we are aware of the relevance of linear assumptions to obtain accurate estimators. Because residual plot evaluation can also be subjective, we followed their suggestion and reran all models with robust linear regression (using the MASS::rlm function in R version 4.4.3 [R Foundation]). While, as expected, there were small differences with the published estimates, all models using robust regression were consistent with what was reported.”

- quote from the reply to a letter to the editor

LM Assumptions: Objective Tests

Calling residual plot evaluation “subjective” is misleading and evasive.

Visual checks are interpretive, but these assumptions objectively testable with quantifiable methods.
This is Statistics 101.

“reran all models with robust linear regression…MASS::rlm”

Robust Linear Regression mainly just down-weights outliers.

Does not deal with non-linearity, heteroskedasticity and non-normality of residuals.

check_model output:

Conclusions Without Supporting Models

“CONCLUSIONS In lean metabolically healthy people on KD, neither total exposure nor changes in baseline levels of ApoB and LDL-C were associated with changes in plaque.”

“there is no association between NCPV vs LDL-C or ApoB and TPS vs LDL-C or ApoB.”

Abstract claim component	Model	Model reported
Δ-plaque vs ΔLDL-C	Δ-NCPV ~ ΔLDL-C	Not reported
Δ-plaque vs LDL-C exposure	Δ-NCPV ~ LDL-C exposure	Not reported
Δ-plaque vs LDL-C baseline	Δ-NCPV ~ LDL-C baseline	Not reported
Δ-plaque vs ΔApoB	Δ-NCPV ~ ΔApoB	Reported
Δ-plaque vs ApoB exposure	Δ-NCPV ~ ApoB exposure	Not reported
Δ-plaque vs ApoB baseline	Δ-NCPV ~ ΔApoB	Reported
N/A	NCPV_final ~ LDL-C exposure	Reported (NCPV_final, PAV_final)

Missing TPS Models and Results

“Results Neither change in ApoB …, baseline ApoB, nor total LDL-C exposure … were associated with the change in noncalcified plaque volume (NCPV) or TPS.”

“Neither … change in ApoB nor the ApoB level … were associated … with TPS (Figures 2D and 2E, Table 3).” - “changes in and baseline levels of ApoB were not associated with changes in NCPV or TPS”

Figures 2D–2F are Δ-TPS (outcome) panels (vs ΔApoB, ApoB, CAC_bl)

Table 3 has no Δ-TPS models

No Δ-TPS ~ LDL-C, LDL-C exposure, or ApoB model results anywhere.

Bayes Factor `rscale` is not Moderate

“Bayes factors were calculated…with default settings and an ~ rscale value of 0.8 to contrast a moderately informative prior with a conservative distribution width (to allow for potential large effect sizes) due to the well-documented association between ApoB changes and coronary plaque changes.”

Calling rscale = 0.8 “moderately informative” is inaccurate.

R package docs: “medium”, “wide”, “ultrawide” = 0.354, 0.5, 0.707

rscaleCont = 0.8 is wider than “ultrawide” → a very diffuse prior that places substantial mass on very large effects
No reported prior-sensitivity to alternative r-scales
Same r-scale apparently used for all models, no justification.

Fixed description:

“We used a very wide prior on coefficients (rscale = 0.8, wider than the package’s”ultrawide”), which places substantial prior mass on very large effects. This diffuse prior penalizes small-to-moderate effects, requiring substantially stronger evidence than under the ‘wide’ or ‘medium’ defaults to support them.”

LDL-C Exposure Calculation

“LDL-C exposure on a KD was calculated by summing the products of the reported days on a KD prior to study commencement and baseline LDL-C on a KD plus the study follow-up days by their final LDL-C.”

\[ \text{LDL-C}_{\text{exp}} = Days_{\text{KD}}\cdot LDL_{\text{baseline}} \;+\; Days_{\text{follow-up}}\cdot LDL_{\text{final}} \]

one baseline value for all pre-study Keto Diet time and one final value for all follow-up is a coarse simplification
relies on recall of KD start

standard AUC/time-weighted approach (need multiple measurements)
limitation due to resources

Lifetime LDL-C Formula Doesn’t Add Up

“LDL-C exposure on a KD was calculated by summing the products of the reported days on a KD prior to study commencement and baseline LDL-C on a KD plus the study follow-up days by their final LDL-C.”

\[ \text{LDL-C}_{\text{exp}} = Days_{\text{KD}}\cdot LDL_{\text{baseline}} \;+\; Days_{\text{follow-up}}\cdot LDL_{\text{final}} \]

“Estimated lifelong LDL-C additionally included the product of age upon commencing a KD and pre-KD LDL-C.”

\[ \text{Life-LDL-C}_{\text{exp}} = Days_{\text{KD}}\cdot LDL_{\text{baseline}} \;+\; Days_{\text{follow-up}}\cdot LDL_{\text{final}} \;+\; \boldsymbol{\big( Age_{\text{at-KD-start}}\cdot LDL_{\text{pre-KD}} \big)} \]

This equation is dimensionally inconsistent.

It adds days and age together. It’s like adding miles and inches.
pre-KD term is down-scaled by ~365× relative to the day-based terms.
any associations with outcomes are dominated by keto diet exposure.
if they did convert age, “lifetime” exposure just reflects how old someone was at KD

This isn’t an Age Mediation Analysis

“Estimated lifetime LDL-C exposure was only a significant predictor of final NCPV in the univariable analysis but lost significance when age was included as a covariate (Table 3). Both age and lifetime LDL-C exposure lost significance when baseline CAC was included in the model (Table 3).”

A mediation analysis:

tests how an exposure affects an outcome through a middle step (the mediator)
estimates an indirect effect (through the mediator) and a direct effect (everything else).
requires a pre-specified pathway and proper statistical testing (usually with CIs or bootstraps).

This is not a mediation analysis.

No indirect effect was estimated or tested.
Age can’t be a mediator of LDL exposure (age isn’t caused by LDL); it’s a confounder.
They only compared p-values after adding variables.

Exposure (E): lifetime LDL-C exposure Mediator (M): baseline CAC (CAC_bl) Outcome (Y): final NCPV Confounder (A): age (affects E, M, and Y)

The mediated/indirect path you’d test is: E → M → Y (LDL exposure → baseline CAC → final NCPV).
When you include M = baseline CAC in the model, you block that E → M → Y path and estimate only the direct effect of E on Y (the E → Y arrow not going through M).

So “Adding baseline CAC blocks the pathway → tests only the direct effect” means: conditioning on baseline CAC removes the indirect route through CAC, leaving only the unmediated E → Y association to be estimated.

What mediation is (A → C through B):

Specify roles: Exposure (A), Mediator (B), Outcome (C).

Fit two models:

B ~ A (+ confounders) → path a

C ~ A + B (+ confounders) → paths b, c′

Report the indirect effect (a×b) with CIs (usually bootstrapped). State assumptions.

Only shows outcome regressions (NCPV_final ~ Age, then + Life-LDL-C_exp, then + CAC_bl).

No mediator model, no indirect effect, no CIs.

The “mediator” (Life-LDL-C_exp) is partly built from Age and mixes units → mathematical coupling; any drop in the Age coefficient can be mechanical.

Age in Exposure, then Control for Age

“Estimated lifetime LDL-C exposure was only a significant predictor of final NCPV in the univariable analysis but lost significance when age was included as a covariate (Table 3). Both age and lifetime LDL-C exposure lost significance when baseline CAC was included in the model (Table 3).”

They ran (reported) three regressions in sequence.

Conclusion: after adjusting for baseline CAC, neither age nor lifetime LDL-C predicts NCPV_final.

- CAC explains the association; age / lifetime LDL-exposure don’t matter.

Changes in p-values come from collinearity due to Age being embedded in lifetime LDL-C exposure.

Age is a confounder/proxy for exposure duration, not a mediator.

CAC association just shows baseline disease predicts future disease.

They did NOT report NCPV_final ~ lifetime LDL-C exposure in the analysis.

they actually did a stepwise covariate adjustment on highly collinear variables and then over-interpreted p-value changes.

“loss of significance” doesn’t show that LDL or Age don’t matter; it shows the model is not set up to answer the mediation/mechanism question.

Intended pathway?: lifetime LDL-C → baseline CAC → NCPV_final.

Age affects all variables.

The “mediator” (Life-LDL-C_exp) is partly built from Age and mixes units → mathematical coupling; any drop in the Age coefficient can be mechanical.

Baseline CAC likely sits on the pathway from long-term LDL exposure to later plaque. Controlling for it can remove the very effect they’re trying to test.

CAC association just shows baseline disease predicts future disease; they don’t establish that age or lifetime LDL exposure don’t matter

Univariable Change Models Can Mislead

“Linear models on the primary (NCPV) and secondary outcomes were univariable”

All conclusions based on independent univariable change score models

Δ-NCPV ~ ApoB; Δ-NCPV ~ NCPV_baseline

Confounding unchecked (age, sex, BP, CAC_bl, baseline plaque)
Δ-NCPV contains baseline NCPV, biasing associations (mathematical coupling)
less power, compounded noise
ignores starting plaque and basics like age/sex
baseline imbalance and shared correlates can inflate, reduce, or reverse associations

Consensus in biostatistics: use ANCOVA style model, follow-up ~ baseline + covariates for pre/post analyses.

NCPV_follow-up ~ NCPV_baseline + ApoB_baseline + age + sex

Next-Year Plaque, Given Your Baseline

ΔNCPV ~ ApoB_baseline (unadjusted change score)

Question: Among all participants, is baseline ApoB associated with the raw change in plaque over 1 year, without accounting for where people started or other factors?

Slope interpretation: Average difference in change (mm³) per 1 mg/dL higher ApoB, unadjusted.

Clinically limited: Doesn’t condition on starting plaque, age, sex, BP; easily distorted by baseline differences and extra noise in change scores.
It doesn’t tell an individual with given baseline/risk profile what their 1-year plaque will be.

NCPV_follow-up ~ NCPV_baseline + ApoB_baseline + age + sex (ANCOVA)

Question: Among people with the same starting plaque, age, sex, and BP, do those with higher ApoB tend to have more plaque at 1 year?

Slope interpretation: Expected difference in 1-year NCPV (mm³) per 1 mg/dL higher ApoB, holding baseline NCPV and covariates fixed.

Clinically relevant: What a patient wants to know; “Given where I start and my risk factors, does higher ApoB mean more plaque next year, and by how much?”

Optionally test ApoB × NCPV_baseline to allow baseline-dependent progression.

Preprint vs Published: What Changed

Pre-print title: Plaque Begets Plaque, ApoB Does Not; Longitudinal Data From the KETO-CTA Trial

Published title: Longitudinal Data From the KETO-CTA Study; Plaque Predicts Plaque, ApoB Does Not

In text: find and replace ‘begets’ with ‘predicts’.

Description of main figure, and primary outcome:

“Most participants presented with stable NCPV (Figures 1A and 1B), with 1 participant exhibiting a decrease in NCPV (Figures 2A to 2C) and 6 participants showing decreases in TPS scores over 1 year”

Removed and replaced with:

“The median change in NCPV was 18.9 mm3 (IQR: 9.3-47.0 mm3) and the median change in PAV was 0.8% (IQR: 0.3%-1.7%).”

In CONCLUSIONS section: “In an exploratory analysis, changes in and baseline levels of ApoB were not associated with changes in NCPV or TPS…”

“exploratory analysis” added in published version. Only mention in entire paper.

Table 1 median (Q1–Q3) PAV at baseline changed from 1.25% (0.5–3.6) to 1.6% (0.5–4.9).

Record of pre-print is unavailable. All links go to new version. It is available here.

Conclusions

Figures, data, and tests don’t match

Key analyses not reported

Modeling choices systematically weaken evidence for an association

Analytic design flaws across multiple analyses

ANCOVA is the clinically relevant model

Quick Hits — Claims vs. Issues

Where	Paper text (claim)	Issue
Figure 1 caption	“…the shaded area represents the IQR …”	Imprecise. IQR is a single number; shaded band is 25th–75th percentile band at baseline and 1-year.
Figure 1 caption	“(9.3–47.0 mm³)”	Wrong context/unstated. Those numbers are IQR of ΔNCPV
Figures 2D–F	“Change in ApoB, baseline ApoB, and baseline CAC vs NCPV.”	Axes/legend appear to be TPS, not NCPV → label/data mismatch
Table 3 caption	“R² = squared correlation coefficient (explained variability).”	Reports negative values, must be adjusted R²
KD Duration Table 1 vs Table 3	KD duration mean 1,642.7 days (≈4.5 y) vs caption “LDL-C exposure … mean 5.7 y.”	Inconsistent durations.
KD Duration Abstract vs Table 1	LDL-C exposure median 1,302 d (984–1,754) vs KD duration median 1,427 d (1,002–1,938).	Metrics conflated. exposure should be in units like mg/dL·days, not days.
Table 1 (Total cholesterol)	Median 338, IQR (301–337).	Impossible IQR (Q3 < median)
Baseline characteristics only	Baseline table provided.	No follow-up characteristics table
Terminology (multiple)	“changes in baseline levels”	Baseline doesn’t change.
Software statement	“using R 4.0.3 (2020)… with the last available version for Sept 2024.”	Unclear what version was used.
Central illustration (quote)	“Neither total exposure nor changes in baseline levels of ApoB and mg/dL were associated… Baseline plaque but ApoB was not associated…”	Incoherent/grammatical errors
Main text (Results/Discussion)	“…baseline values magnify their percentual changes…”	percent change or percentage-point change

Nonstandard Percent Change

“The median change in NCPV was 18.9 mm3 (IQR: 9.3-47.0 mm³) and the median change in PAV was 0.8% (IQR: 0.3%-1.7%). Compared to baseline, these represent a 43% and 50% change, respectively.”

This isn’t the standard subject-level percent change.

They computed a ratio of median change to baseline median: \(\frac{\operatorname{median}(NCPV_{1y}-NCPV_{bl})}{\operatorname{median}(NCPV_{bl})}\times 100\%\)

NCPV: \(18.9/44 \approx 43\%\); and PAV: \(0.8/1.6 \approx 50\%\)

Standard percent change: \(\operatorname{median}\!\left(\frac{NCPV_{1y}-NCPV_{bl}}{NCPV_{bl}}\right)\times 100\%\)

“What was the typical relative change per subject?”

Standard percent change vs. reported ratio-of-medians:

Outcome	“ratio-of-medians”	Median % change	Mean % change
NCPV	43%	49.2%	81.4%
PAV	50%	47.3%	80.7%

Their “percent change” metric is mislabeled, nonstandard and not well explained.

Plaque Metrics Summary Table

Baseline, follow-up, and paired change in plaque metrics at 1 year
Metric	N¹	Median (Q1–Q3)			Mean ± SD
Metric	N¹	Baseline	Follow-up	Change²	Baseline	Follow-up	Change²
Noncalcified plaque volume (mm³)	100	44.0 (15.5–102.2)	66.0 (25.2–163.2)	18.8 (9.3–46.6)	75.9 ± 88.3	107.4 ± 112.7	31.5 ± 31.5
Coronary artery calcium score	100	0.0 (0.0–54.2)	0.0 (0.0–56.0)	0.0 (0.0–5.0)	50.3 ± 100.9	58.8 ± 120.4	8.5 ± 25.5
Percent atheroma volume (%)	100	1.6 (0.5–5.0)	2.6 (1.0–6.8)	0.8 (0.3–1.7)	3.2 ± 3.8	4.4 ± 4.6	1.2 ± 1.2
Total plaque score	100	0.0 (0.0–2.2)	1.0 (0.0–3.0)	0.0 (0.0–1.0)	1.7 ± 2.6	2.2 ± 3.0	0.5 ± 1.1
Calcified plaque volume (mm³)	100	0.3 (0.0–19.8)	0.9 (0.0–24.2)	0.5 (0.0–4.2)	18.7 ± 37.4	22.7 ± 42.5	4.0 ± 7.4
¹ N = number of paired scans per metric.
² Change = follow-up − baseline, summarized across participants.